Algebraic Expressions 2x + 3y - 7

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Presentation transcript:

Algebraic Expressions 2x + 3y - 7 What are the Terms?

Algebraic Expressions 2x + 3y - 7 Terms

Algebraic Expressions 2x + 3y - 7 What are the coefficients?

Algebraic Expressions 2x + 3y - 7 Coefficients

Algebraic Expressions 2x + 3y - 7 What is the constant?

Algebraic Expressions 2x + 3y - 7 Constant

Algebraic Expressions 2x + 3y - 7 What are the operators?

Algebraic Expressions 2x + 3y - 7 Operator

Algebraic Expressions Polynomial: monomial → x, 2xy, 4, 3x²y, … single term binomial → x+1, 2xy+x, 3x²y+4, …two terms trinomial → 2x+3y+7, 3x²y+xy+4x, …three terms polynomial → …four or more terms Caution: polynomials do not contain division by a variable! Example: 3x/y + 4 is not a polynomial.

Evaluating Algebraic Expressions

Evaluate the following algebraic expression using x=9, y=1 x-(x-(x-y³))

Answer: 8

Simplifying Algebraic Expressions

Simplify the following algebraic expression: -3p + 6p

Answer: 3p

Simplify the following algebraic expression: 7x - x

Answer: 6x

Simplify the following algebraic expression: -10v + 6w

Answer: -10v + 6w

Simplify the following algebraic expression: b - 3 + 6 - 2b

Answer: -b + 3

Simplify the following algebraic expression: 10x-w+4y-3x+36-38x-47+32x+2w-3y

Answer: w+x+y-11

Simplify the following algebraic expression using the distributive property:

Answer: -2 + 10v

Simplify the following algebraic expression using the distributive property: (3 - 7k) ∙ (-2)

Answer: -6 + 14k

Simplify the following algebraic expression using the distributive property: 7n(6n + 3)

Answer: 42n² + 21n

Simplify the following algebraic expression using the distributive property:

Answer: 5 + 21b

Simplify the following algebraic expression using the distributive property: 3n(n² - 6n + 5)

Answer: 3n³ - 18n² + 15n

Simplify the following algebraic expression using the distributive property: 2k³(2k² + 5k - 4)

Answer: 4k⁵ +10k⁴ - 8k³

Simplify the following algebraic expression using the distributive property: 9v²(u² + uv - 5v²)

Answer: 9v²u² +9v³u – 45v⁴

Simplify the following algebraic expression using the distributive property: 3x(5x+2) - 14(2x²-x+1)

Answer: -13x² + 20x - 14

Simplify the following algebraic expression using the distributive property: x(x+2) - 3(x+2)

Answer: x² - x - 6

Expand and simplify using the FOIL method: (x-3)(x+2)

Answer: x² - x - 6

Factor the following algebraic expression: x² + 4x + 4

Answer: (x+2)·(x+2) or (x+2)2

Simplify completely: y5 y-3 ( )½

Answer: y4

Simplify completely: 3x² - 6 9

Answer: x² - 2 3

Simplify completely: a³ - a a⁴ - a²

Answer: 1 a

Simplify completely: 18 – 36x 2 – 4x

Answer: 9

Simplify completely: 3x 4x – 4 9x² x - 1

Answer: 1/12x

Write the following as a single fraction: 3x 11 5 40x -

Answer: 24x2 – 11 40x

Write the following as a single fraction:

Answer: 2 – x 2x2+2x

Write the following as a single fraction: a³ - a 7a³ a² - 1 49a⁴ -

Answer: 7a - 1 7a

Write the following as a single fraction: 1 1 z² + 1 z² -

Answer: 1 z⁴ + z² -

Write the following as a single fraction: 3x 11 5 40x -

Answer: 24x2 – 11 40x